Q: In Eratosthenes' experiment, the angle of the Sun's rays at Alexandria was measured to be $$7.2^\circ. If $$the distance between Syene and Alexandria is 800 km, what formula did he use to calculate the Earth's circumference $$C$$?

$$C = \dfrac{360^\circ}{7.2^\circ} \times 800\ \text{km}$$

Question 1

Which of the following best describes why Eratosthenes was able to measure the circumference of the Earth over 2000 years ago?

Accepted Answer

He used the difference in the angle of the Sun's rays at two different locations at the same time.

Question 2

In Eratosthenes' experiment, the angle of the Sun's rays at Alexandria was measured to be $$7.2^\circ. If $$the distance between Syene and Alexandria is 800 km, what formula did he use to calculate the Earth's circumference $$C$$?

Accepted Answer

$$C = \dfrac{360^\circ}{7.2^\circ} 	imes 800\ 	ext{km}$$

Question 3

Why is it important that scientific hypotheses are testable and falsifiable?

Accepted Answer

Because only testable and falsifiable hypotheses can be evaluated by experiments or observations.

Question 4

A scientist wants to measure the diameter of the Sun using the method described in the notes. Which of the following measurements does she need?

Accepted Answer

The distance from the Earth to the Sun and the diameter of the Sun's image through a pinhole.

Question 5

Which of the following is NOT a step in the scientific method as described in the lecture notes?

Accepted Answer

Accepting a hypothesis without testing.

Question 6

If the angle measured at Alexandria was $$7.2^\circ$$ and the distance between Syene and Alexandria was 800 km, what value did Eratosthenes calculate for the Earth's circumference?

Accepted Answer

$$40,000\ 	ext{km}$$

Question 7

Which of the following statements about scientific measurements is most accurate?

Accepted Answer

They are a method of quantifying observations to better understand natural phenomena.

Question 8

A hypothesis states, 'All swans are white.' Which of the following would falsify this hypothesis?

Accepted Answer

Observing a single black swan.

Question 9

In the method for measuring the Sun's diameter, which equation relates the diameter of the Sun $$d to $$the diameter of the Sun's image $$D$$ and the distances involved?

Accepted Answer

$$\dfrac{d}{D} = \dfrac{L}{l}$$

Question 10

Which of the following best illustrates the application of the scientific method?

Accepted Answer

A researcher observes a pattern, proposes a hypothesis, predicts results, tests the hypothesis, and formulates a general rule.

Question 11

Why did Eratosthenes need to know the distance between Syene and Alexandria for his experiment?

Accepted Answer

To calculate the proportion of Earth's circumference corresponding to the measured angle.

Question 12

Which of the following is a requirement for a statement to be considered a scientific hypothesis?

Accepted Answer

It must be testable and falsifiable.

Question 13

Suppose you measure the angle of the Sun's rays at two locations 500 km apart and find a difference of $$5^\circ. $$What is the calculated circumference of the Earth?

Accepted Answer

$$C = \dfrac{360^\circ}{5^\circ} 	imes 500\ 	ext{km} = 36,000\ 	ext{km}$$

Question 14

Which of the following is an example of a hypothesis that is NOT falsifiable?

Accepted Answer

"Invisible unicorns exist somewhere in the universe."

Question 15

What is the main reason that the scientific method is considered reliable for gaining knowledge about the natural world?

Accepted Answer

It relies on systematic observation, experimentation, and the ability to test and falsify hypotheses.

Ch 01 – About Science: Scientific Measurements and Methods

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